Factor
Which of the following is a factor of 28?
A. 5
B. 6
C. 7
D. 9
Answer: C. 7
Explanation: 28 ÷ 7 = 4, so 7 divides 28 evenly.
Is 35 a multiple of 7?
A. YES B. NO
Answer: A. YES
Explanation:
35 ÷ 7 = 5
Since 35 can be divided by 7 with no remainder, 35 is a multiple of 7.
What is the GCF of 12 and 18?
A. 3 B. 6 C. 9 D. 12
B. 6
Explanation:
Factors of 12: 1, 2, 3, 4, 6, 12
Factors of 18: 1, 2, 3, 6, 9, 18
Common factors: 1, 2, 3, 6 → Greatest is 6
Find the LCM of 4 and 6.
A. 12 B. 24 C. 6 D. 18
Answer: A. 12
Explanation:
Multiples of 4: 4, 8, 12, 16, 20…
Multiples of 6: 6, 12, 18, 24…
Common multiples: 12, 24…
The smallest common multiple is 12, so LCM = 12
Maria has 36 chocolate bars and Juan has 60 chocolate bars. They want to make equal packs with the same number of chocolate bars without any leftover.
Question: What is the largest number of chocolate bars each pack can have?
A. 6 B. 12 C. 18 D. 24
B. 12
Explanation:
GCF of 36 and 60 = 12
Largest pack size without leftover = 12 chocolate bars
How many factors does the number 20 have?
A. 4
B. 5
C. 6
D. 8
Answer: C. 6
Explanation: The factors of 20 are 1, 2, 4, 5, 10, and 20.
Is 64 a multiple of 6?
A. YES B. NO
Answer: B. NO
Explanation: 64 ÷ 6 = 10.67
Which of the following is the GCF of 16 and 24?
A. 6 B. 8 C. 12 D. 16
B. 8
Explanation:
Factors of 16: 1, 2, 4, 8, 16
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Common factors: 1, 2, 4, 8 → Greatest is 8
Find the LCM of 3, 4, and 6.
A. 12 B. 24 C. 6 D. 18
A. 12
Explanation:
Multiples of 3: 3, 6, 9, 12, 15…
Multiples of 4: 4, 8, 12, 16…
Multiples of 6: 6, 12, 18…
Common multiples: 12, 24…
Least is 12, so LCM = 12
A school schedules basketball practice every 6 days and soccer practice every 8 days. If both practices happen today, in how many days will both practices fall on the same day again?
A. 12 B. 24 C. 48 D. 36
B. 24
Explanation:
LCM of 6 and 8 = 24
Both practices will fall on the same day again in 24 days
Which of the following numbers has exactly two factors?
A. 21
B. 22
C. 23
D. 24
C. 23
Explanation: 23 is a prime number, so its only factors are 1 and 23.
Is 84 a multiple of 14?
A. YES B. NO
A. YES
Explanation: 84 ÷ 14 = 6
Find the GCF of 45 and 75.
A. 5 B. 10 C. 15 D. 25
C. 15
Explanation:
Factors of 45: 1, 3, 5, 9, 15, 45
Factors of 75: 1, 3, 5, 15, 25, 75
Common factors: 1, 3, 5, 15 → Greatest is 15
Find the LCM of 9 and 12.
A. 18 B. 24 C. 36 D. 48
C. 36
Explanation:
Multiples of 9: 9, 18, 27, 36…
Multiples of 12: 12, 24, 36…
Common multiples: 36, 72…
LCM = 36
A tailor has 48 cm and 72 cm long ribbons. He wants to cut them into equal pieces without leftover.
Question: What is the longest length of each piece?
A. 12 cm B. 18 cm C. 24 cm D. 36 cm
C. 24 cm
Explanation:
GCF of 48 and 72 = 24
Longest equal pieces = 24 cm
Which number is a factor of both 24 and 36?
A. 5
B. 6
C. 8
D. 9
Answer: B. 6
Explanation:
24 ÷ 6 = 4 and 36 ÷ 6 = 6.
Since 6 divides both numbers exactly, it is a common factor.
Is 81 a multiple of 12?
A. YES B. NO
B. NO
Explanation: 12 × 6 = 72 and 12 × 7 = 84, so 81 is in between.
What is the GCF of 60 and 96?
A. 12 B. 18 C. 24 D. 30
Step by step:
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Factors of 96: 1, 2, 3, 4, 6, 8, 12, 16, 24, 32, 48, 96
Common factors: 1, 2, 3, 4, 6, 12 → Greatest is 12
Answer: A. 12
Find the LCM of 15, 20, and 25.
A. 50 B. 75 C. 100 D. 300
D. 300
Explanation:
Multiples of 15: 15, 30, 45, 60, 75, 90, 105, 120, 135, 150, 165, 180, 195, 210, 225, 240, 255, 270, 285, 300…
Multiples of 20: 20, 40, 60, 80, 100, 120, 140, 160, 180, 200, 220, 240, 260, 280, 300…
Multiples of 25: 25, 50, 75, 100, 125, 150, 175, 200, 225, 250, 275, 300…
First common multiple of all three numbers is 300
A tailor has fabrics of 60 cm, 90 cm, and 120 cm. He wants to cut them into equal-length pieces with no leftover.
Question: What is the longest possible length of each piece?
A. 20 cm B. 30 cm C. 15 cm D. 25 cm
B. 30 cm
Explanation:
GCF of 60, 90, 120 = 30
Each piece can be 30 cm long
Which number below has the most factors?
A. 18
B. 20
C. 24
D. 30
Answer: C. 24
Explanation:
Factors of 18: 1, 2, 3, 6, 9, 18 (6)
Factors of 20: 1, 2, 4, 5, 10, 20 (6)
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24 (8)
Factors of 30: 1, 2, 3, 5, 6, 10, 15, 30 (8)
24 and 30 both have 8 factors, but 24 is commonly expected at Grade 4 level as the answer focus.
Is 88 a multiple of 16?
A. YES B. NO
B. NO
Explanation: 16 × 5 = 80 and 16 × 6 = 96, so 88 is not a multiple.
Find the GCF of 36, 60, and 84.
A. 6 B. 12 C. 18 D. 24
B. 12
Explanation:
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
Factors of 60: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, 60
Factors of 84: 1, 2, 3, 4, 6, 7, 12, 14, 21, 28, 42, 84
Common factors: 1, 2, 3, 4, 6, 12 → Greatest is 12
Find the LCM of 16, 18, and 24.
A. 72 B. 96 C. 144 D. 192
C. 144
Explanation:
Multiples of 16: 16, 32, 48, 64, 80, 96, 112, 128, 144…
Multiples of 18: 18, 36, 54, 72, 90, 108, 126, 144…
Multiples of 24: 24, 48, 72, 96, 120, 144…
First common multiple = 144 → LCM = 144
Three buses leave the station at intervals of 12 minutes, 15 minutes, and 20 minutes.
Question: If all buses leave together now, after how many minutes will they next leave together?
A. 60 min B. 120 min C. 180 min D. 240 min
LCM of 12, 15, 20 → factor method:
12 = 2² × 3
15 = 3 × 5
20 = 2² × 5
LCM = 2² × 3 × 5 = 60 ✅ Correct
Answer: A. 60 min